Gravitational Potential Field

[Progenitor A]

Gravitational Potential Field is simply another way of describing/measuring the gravitational field (indeed it can be considered as a primary measure as the gravitational acceleration field is a derivative of the magnitude of this scalar quantity), so there are at least two ways of defining the gravitational field. (This caused some confusion - to me - on a previous thread)

Shown below is a plot of the gravitational potential of the earth with the horizontal axis showing multiples of earth radius and the vertical axis showing the Gravitational potential. - when the gravitational potential is about zero we are effectively out of the earth's gravitational field and this occurs at > 20 earth radius's, conversely the nearer we move to the earth so th e(negative) magnitude of the gravitational potential field increases




An interesting point about this diagram is that if we revolve the graph around the vertical axis to get a 3D model of the gravitational potential, it is almost identical (perhaps identical?) to the curved space-time diagrams we are all familiar with

[carnyx]

Progenitor A,

If the function of your graph is of the form 1/ (x- squared) then it has the same form as a graph of the weight-change with distance of a given mass.

[abacus9900]

...when the gravitational potential is about zero we are effectively out of the earth's gravitational field and this occurs at > 20 earth radius's, conversely the nearer we move to the earth so th e(negative) magnitude of the gravitational potential field increases.

This would make sense, naymissus, when you consider than the gravitational potential is equal to mass x gravity (9.8 mtrs. per second per second) x height. Obviously, the less the value of gravity the less the gravitational potential in this equation.

[Progenitor A]

Oct 11, 2010 10:43:34 GMT 1 carnyx said:

Progenitor A,

If the function of your graph is of the form 1/ (x- squared) then it has the same form as a graph of the weight-change with distance of a given mass.

This one is -1/x Carnyx

[speakertoanimals]

Looking at gravitational potential allows you to make links with other field theories, such as electromagnetism. So, for a single charge, the electric potential goes as 1/r, just like gravity. Except unlike gravity, the electric potential can either increase or decrease, depending on the SIGN of the charge. Which just says that unlike gravity, electrostatic forces can either attract (unlike charges), or repel (like charges). Gravity only attracts.

WHY 1/r? Why 1/r^2? Well, turns out that potential isn't necessarily the best way to do this. Think of electric fields and electric flux. We are all used to magnets and magnetic flux lines, traced out by iron filings. We can have electric flux lines as well, which start off on positive charges, and radiate out until they find a negative charge. So, for a single charge, with flux just radiating outwards, we see that since in 3D area of a sphere goes as r^2, so flux density goes as 1/r^2. Hence field strength = flux density gives us the basic 1/r^2 field of force.

[Mr Red]

gravity is a 3D vector.

It acts on Earth, not to the geometric centre but to the centre of mass which is the same as the centre of gravity. Satellites have to take into account the non-homogeniusness of the Earth. NASA refers to masscons (Mass Concentrations) which might be buried asteroidal type thingies (hence the Moon) or mountains. And continents - it is a density thing.

I used to design weighing machines and spring (eg strain gauge/loadcells) ballances were sensitive to lattitude (oblate Earth) and mountains. Not to mention the Moon - approx 1/10000, Sun 1/100000 and mountains. We never got past the moon accuracy.

[Progenitor A]

Oct 18, 2010 10:38:13 GMT 1 Mr Red said:

I used to design weighing machines ......

So it was you!
I once paid a shilling and stood on one of those thingys and it said ' F Off You fat b*st*rd'!

[Mr Red]

Weren't one of mine, we programmed it to say "One at a Time please".